Tag Archives: Hipparchus

Weil der Stadt is located near Stuttgart. Johannes Kepler was born in this very veautiful town on December 27, 1571 and his memory is still there: this big statue is in the middle of the Market Square…

Photography by Carlos Dorce

… and Copernicus, Mästlin, Tycho Brahe and Jobst Bürgi are with him in this monumental sculpture.

Photography by Carlos Dorce

The four scientists are in the corners of the base of the statue and the words “Astronomia”, “Optica”, “Mathematica” and “Physica” are graved on each of the four sides.

Photography by Carlos Dorce

I must say that here we have the first (imaginary) bust of Bürgi that I know. Bürgi was one of the originators of the logarithms because Kepler said that he had seen Bürgi using logarithms in astronomical calculus (Rudolphine Tables (1627)) before their “official” first occurrence in Napier’s Mirifici Logarithmorum Canonis Descriptio (1614). Furthermore, Bürgi published his logarithms in his Aritmetische und Geometrische Progreß tabulen (1620) but his “red numbers” and “black numbers” couldn’t never win the “logarithms” which were the first calculator in all history.

Photography by Carlos Dorce

Notice that this statue is not very similar to this other portrait from 1620:

J.Bürgi at the age of 67. Drawing by Aegidius Sadeler (1619)

The base of the statue also have four graved images representing moments in Kepler’s life like thispicture with Kepler in the middle explaining the Copernican system…

Photography by Carlos Dorce

… with Hipparchus and Ptolemy watching how a central Sun brights in the middle of the universe.

Can you imagine Kepler investigating about his elliptical orbits?

Photography by Carlos Dorce

Next to Market Square there is his bithplace which hosts… no, no, no! Tomowwor will be another day!

In a previous post I began to talk about this museum located inside Frombork castle. You can learn almost everything about him, his life and his works on medicine, economies and, of course, astronomy, including the replicas of his instruments (we saw them also in Warsaw). For example, it’s possible to see some facsmile editions of his works and also a recreation of his desk:

Photography by Carlos Dorce

Among the references about his publication of his works, we can find this engraving showing Copernicus in a lecture for the Cracovian scientists in 1509:

Photography by Carlos Dorce

Or this other wonderful one (1873) with Copernicus in he middle of the picture talking about his heliocentric system:

Photography by Carlos Dorce

How proud he is ofhisheliocentric theory!

Photography by Carlos Dorce

And who are his guests? First of all, Hipparcus (with the armillar spher) and Ptolemy (with his geocentric system) are listening the theory which will finish theirs. Ptolemy looks askance at Tycho Brahe meanwhile Newton is looking at Laplace:

Photography by Carlos Dorce

Galileo Galilei is behind Copernicus looking at him with great reverence:

Photography by Carlos Dorce

And Hevelius, the other great Polish astronomer, agrees Copernicus’ theories although he never had the telescope to check them.

Photography by Carlos Dorce

Finally, Johannes Kepler seems to be bored of listening this obvious theory although his ellipses will be the curves which will change the astronomy.

The Long Market (Długi Targ) is one of the most important touristic attractions of Gdansk. It was a merchant road in the 13th century. After the massacre of Gdansk citizens on 13 November 1308 by Teutonic Knights, the place became the main street of the city and is name “Longa Platea” was first written in 1331. Nowadays it’s a very beautiful long square full of typical shops and restaurants which are the soul of this cosmopolutan city. One of its most representative houses is the town hall from the 16th century and Neptune’s Fountain, the main symbol of the city, is also there. This fountain was constructed in 1617 from Abraham van den Blocke’s designs.

Photography by Carlos Dorce

Thus, if you visit Gdansk, you must have time to take a beer or a coffee in one of the cafes or have a typican Polish dinner in one of the restaurants which fill all the beautiful houses which can be admire in the square.

Among all these houses we also find a lot of mathematical symbols which allow me to talk of them in this new post. For example, Radisson Blue hotel is located in number 19 and the allegorical paintings of the facade are a joy for the mathematical freak:

Photography by Carlos Dorce

On both sides we have some of the most important men in the history of astronomy like Hipparcus of Rhodas,

Photography by Carlos Dorce

Ptolemy:

Photography by Carlos Dorce

Copernicus:

Photography by Carlos Dorce

Galileo Galilei:

Photography by Carlos Dorce

and Hevelius:

Photography by Carlos Dorce

Approaching the town hall, there is another red house which is full of artists ans it’s coronated by a replica of Aristotle and Plato from Raffaello’s “School of Athens”:

Photography by Carlos Dorce

In another house there also are the allegorical Astronomia rounded by Cellarius’ heliocentric systems:

Photography by Carlos Dorce

And finally we find other allegories like the Architecture, the Geometry or the Geography in the opposite side of the square:

Photography by Carlos Dorce

For example…

Photography by Carlos Dorce

…or:

Photography by Carlos Dorce

As you can see, this isan excuseto admirethe beautifulfacades ofthe houses in thissquare whichI never tireof walking throughit.

One of the most beautiful buildings which can be visited in Zaragoza is the hall of the former Faculty of Sciences. Itwas constructed by Ricardo Magdalena in 1893 and is decorated with 72 statues and roundels designed by Dionisio Lasuén (1850-1916). These allegorical sculptures are dedicated to Medicine and Science and we find some very important mathematicians among all the scientifics represented on them. For example:

Photography by Carlos Dorce

We also fins a representation of the Theorem of Pythagoras next to these two great names:

Photography by Carlos Dorce

Other important mathematicians are:René Descartes…

Photography by Carlos Dorce

…Galileo Galilei…

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…the great Euclid…

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…Hipparchus of Rhodes…

Photography by Carlos Dorce

We also find Spanish scientific and mathematicians as the Andalusi Abû al-Qâsim al-Zahrawî (Al-Zahra, Cordova,936-Cordoba,1013), also known as Abulcasis. He was an important physician, surgeon and doctor who wrote the Kitab at-Tasrif (Arabic,كتاب التصريف لمن عجز عن التأليف) or The Method of Medicine (compiled in 1000 AD) which had an enormous impact in all Medieval Europe and the Islamic World.

Photography by Carlos Dorce

Pedro Sanchez Ciruelo (Daroca,1470 – Salamanca, 1550) was an important Spanish mathematician of the 16th century who wrote some mathematical treatiseslike the Cursus quattuor mathematicarum artium liberalium (1516) thorugh which Bradwardine’s Arithmetic and Geometric work was taught in Spain.

Pedro Sánchez Ciruelo (1470-1550)

Jorge Juan (1713-1773) and Antonio Ulloa (1716-1795) were two Spanish scientifics who participated in the measurement of the Terrestrial Meridian organized by the Academy of Sciences of Paris:

Photography by Carlos Dorce

Gabriel Ciscar (1759-1829) wrote the Curso de Estudios Elementales de la Marina, divided in a volume dedicated to Arithmetics and another dedicated to Geometry.

Photography by Carlos Dorce

Finally, José Rodríguez González (1770-1824) and José Chaix (1765-1811) participated in the triangulations of the meridian arc from Dunkerque to Barcelona.Furthermore,Chaix wrote the Instituciones de Cálculo Diferencial e Integral and publicó the Memoria sobre un nuevo método general para transformar en serie las funciones trascendentes which were so popular in Spain because of the explanations of the differential calculus.

Photography by Carlos Dorce

So, the building is so beautiful and you can learn History of Mathematics while walking around it. Do you want anything else?

This is not the first time in which I talk about Justus van Gent’s paintings. Indeed, the first post of this blog was dedicated to the portrait of Euclid of Alexandria made by this Dutch painter. This portrait is in Louvre Museum and it’s part of the serie of portraits of some important people made by Van Gent.

Claudius Ptolemy lived and worked in the IInd century AD in Alexandria. We know little about him and we can place his life from his own astronomical observations recorded in his great work entitled Mathematical Collection. His first observation was an eclipse of the Moon made in Alexandria in the 5 April of 125 AD and the last one was the observation of the maximum elongation of Mercury made in the 2 February of 141 AD. This recorded data mean that Ptolemy worked in his astronomical book in the period 125-141 AD. Furthermore, we know that in the year 147/148 AD he erected a stele in the town of Canopus about 25 Km East of Alexandria. we can also observe that his name Claudius Ptolemy is a good definition of his life: Claudios is a Greek name whereas Ptolemaios could indicate that he came from one of the various Egyptian towns named after the Ptolemaic kings.

Ptolemy’s Mathematical Collection was the most important Greek astronomical work. Later the Arabs called it with the superlative Al-Majistî (Almagest) and with this name the Latin Europe adopted as the referencial astronomical handbook. In the IVth century, Pappus of Alexandria (c.290-c.350) made a Commentary on it and part of the commentary on Book V (the Almagest is divided in 13 Books) as well as his commentary on Book VI are actually extant in the original. Theon of Alexandria (c.335–c. 405) wrote another commentary on the Mathematical Collection in 11 books incorporating as much as was available of Pappus’ work. Theon was assisted by his daughter Hypatia of Alexandria (c.360–March 415) and the whole text was published at Basel by Joachim Camerarius (April 12, 1500 – April 17, 1574) in 1538.

Joachim Camerarius (1500-1574)Font: Wikimedia Commons

The Mathematical Collection arrived at the Muslim World and it was translated into Arabic, first by translators unnamed at the instance of Yahyâ b. Khâlid b. Barmak, then by al-Hajjâj, the translator of Euclid (c.786-835), and again by Ishaq b. Hunain (d.910) whose translation was improved by Thâbit b. Qurra (c.826–February 18, 901). The first edition to be published (Venice, 1515) was the Latin translation made by Gherard of Cremona from the Arabic, which was finished in 1175. Although there was a previous Latin translation from the Greek, the first Latin translation from the Greek to be published was that made by Georgius of Trebizond in 1451 and the editio princeps of the Greek text was brought out by Grynaeus at Basel in 1538.

According to Sir Thomas Heath in his A History of Greek Mathematics (II, 275), the Almagest is most valuable for the reason that it contains very full particulars of observations and investigations by Hipparchus, as well as of the earlier observations recorded by him. The indispensable preliminaries to the study of the Ptolemaic system, general explanations of the different motions of the heavenly bodies in relation to the Earth as centre, propositions required for the preparation of Tables of Chords, the Table itself, some propositions in spherical trigonometry,… are in Books I and II; Book II deals with the length of the year and the motion of the Sun on the eccentric and epicycle hypotheses; Book IV is about the length of the months and the theory of the Moon; in Book V we find the construction of an astrolabe and the theory of the Moon continued, the diameters of the Sun, the Moon and the Earth’s shadow, the distances between them and their dimensions; the conjunctions and oppositions of Sun and Moon, the solar and lunar eclipses and their periods are studied in Book VI; Books VII and VIII are about fixed stars and the precession of the equinoxes and Books IX-XIII are devoted to the movements of the planets.